Question

2a: An electron and a proton have parallel velocities Up and ve (below left). Determine the direction of the magnetic force on the electron due to the proton and determine the direction of the magnetic force on the proton due to the electron. Are these directions opposite each other? In other words, do they seem to satisfy Newton's 3rd Law? (In this case, the magnitudes of both forces are the same.) b: This time we have three protons traveling with velocity along a straight line and an electron with velocity ve which is perpendicular to that line (below right). The dots repre- sent the exact locations of the charges. Determine the direction of the magnetic force on the electron due to each proton. Then determine the direction of the magnetic force on each proton due to the electron. This time the forces between each pair of charges are clearly not in opposite directions. The point is that Newton's 3rd Law is not necessarily satisfied for forces which depend upon velocity! e p e p pi р

Answer 1

Р La q into now e and in direction. now cause By right hand rule Since proton is moving rightwand direction, So if we point thumb in right direction Curlig og fingers at position e if magustin fonce, ff - q cuxo) Since moving in î o it in (-²) change on elutron is-e. fo is -chx (-2) = So magnetic force é in - é will magnetic field for Proton. magnetic field is in to the page af since Change is negative on el So & magnetic field in - ² & & magnetic force on proton is in direction Cocx (-²) So magnetic force on proton in yes direction is opposite to each other. Since Magnetic face magnitude is depending Charge, velocity & mgnetic field dane in magnitude for both Eletto and proton. Hence é de exert equal and opposite force one each other de they newton's third low. directish. which Follow

(b) fé 2 P ow 1 Р Direction ît the of force on el Magnetic field is given by dB = 40 2 1 (Wxh) unit vector from moving change to location for each of 3 protona positim vector in will have a positive ŷ components So magnetic field direction = Gê x ) = ? magnetic force -elu x B) e ŷ x 3 J =- é will experience all 3 proton now herung x de - direction magnetre force in due to

Now, force force on proton! velocity of e = ve Since d&= Moq Luxa) UIT re ya - for - direction z So first proton, =) Magnetic field Tŷx (-2-} farce direction = q (W x 8 ) = Cêx - ²) = first proton force in ý so

nd 2 مي So - for 2 proton. and direction direction of magnetic field = - Cŷx (-91) o magnetic fane for and proton. h = od clination=-e (ů x B) - Cŷ x(-9) 슨 majestic force directions direction = q lux B y magnetic fance on third proton in -ý. so magnetic field Z so Ezê x2) So